Best 1208 quotes in «math quotes» category

Data Science takes the guesswork/emotions out of answering business questions by applying logic and mathematics to find better solutions.

Do not try the parallels in that way: I know that way all along. I have measured that bottomless night, and all the light and all the joy of my life went out there. [Having himself spent a lifetime unsuccessfully trying to prove Euclid's postulate that parallel lines do not meet, Farkas discouraged his son János from any further attempt.]

Don't dismiss Simplicity, simple is solid.

Education makes your maths better, not necessarily your manners.

Excel suffers from an image problem. Most people assume that spreadsheet programs such as Excel are intended for accountants, analysts, financiers, scientists, mathematicians, and other geeky types. Creating a spreadsheet, sorting data, using functions, and making charts seems daunting, and best left to the nerds.

Eureka!" Mungo yelled. It was a word that wasn't actually a word but which he'd mathematically proved to exist in a parallel realm and he quite liked the sound of it when it came to needing something to yell in moments of cerebral triumph.

Einstein, twenty-six years old, only three years away from crude privation, still a patent examiner, published in the Annalen der Physik in 1905 five papers on entirely different subjects. Three of them were among the greatest in the history of physics. One, very simple, gave the quantum explanation of the photoelectric effect—it was this work for which, sixteen years later, he was awarded the Nobel prize. Another dealt with the phenomenon of Brownian motion, the apparently erratic movement of tiny particles suspended in a liquid: Einstein showed that these movements satisfied a clear statistical law. This was like a conjuring trick, easy when explained: before it, decent scientists could still doubt the concrete existence of atoms and molecules: this paper was as near to a direct proof of their concreteness as a theoretician could give. The third paper was the special theory of relativity, which quietly amalgamated space, time, and matter into one fundamental unity. This last paper contains no references and quotes to authority. All of them are written in a style unlike any other theoretical physicist's. They contain very little mathematics. There is a good deal of verbal commentary. The conclusions, the bizarre conclusions, emerge as though with the greatest of ease: the reasoning is unbreakable. It looks as though he had reached the conclusions by pure thought, unaided, without listening to the opinions of others. To a surprisingly large extent, that is precisely what he had done.

For the first time in his life, he decided to focus on his math homework.

For other great mathematicians or philosophers, he used the epithets magnus, or clarus, or clarissimus; for Newton alone he kept the prefix summus.

Grammar is like your overarching compulsion. It’s math with words.

For we may remark generally of our mathematical researches, that these auxiliary quantities, these long and difficult calculations into which we are often drawn, are almost always proofs that we have not in the beginning considered the objects themselves so thoroughly and directly as their nature requires, since all is abridged and simplified, as soon as we place ourselves in a right point of view.

From the age of 13, I was attracted to physics and mathematics. My interest in these subjects derived mostly from popular science books that I read avidly. Early on I was fascinated by theoretical physics and determined to become a theoretical physicist. I had no real idea what that meant, but it seemed incredibly exciting to spend one's life attempting to find the secrets of the universe by using one's mind.

Further, the same Arguments which explode the Notion of Luck, may, on the other side, be useful in some Cases to establish a due comparison between Chance and Design: We may imagine Chance and Design to be, as it were, in Competition with each other, for the production of some sorts of Events, and many calculate what Probability there is, that those Events should be rather be owing to the one than to the other.

He calculated the number of bricks in the wall, first in twos and then in tens and finally in sixteens. The numbers formed up and marched past his brain in terrified obedience. Division and multiplication were discovered. Algebra was invented and provided an interesting diversion for a minute or two. And then he felt the fog of numbers drift away, and looked up and saw the sparkling, distant mountains of calculus.

Half and half equals one. And if already divided, Left they are as two halves For they're broken hearted.

Here is an equation worth remembering: Five dollars earned minus seven dollars spent = Unhappy Life." (Life Hacks, p.51)

Human beings are more or less formulas. Pun intended. We are not any one thing that is mathematically provable. We are more or less than we are anything. We are more or less kind, or more or less not. More or less selfish, happy, wise, lonely.

However, as I hope to persuade you, there are some interesting connections between science and magic. They share a belief, as one mathematician put it, that what is visible is merely a superficial reality, not the underlying "real reality." They both have origins in a basic urge to make sense of a hostile world so that we may predict or manipulate it to our own ends.

I am no friend of probability theory, I have hated it from the first moment when our dear friend Max Born gave it birth. For it could be seen how easy and simple it made everything, in principle, everything ironed and the true problems concealed. Everybody must jump on the bandwagon [Ausweg]. And actually not a year passed before it became an official credo, and it still is.

I don't see how it's doing society any good to have it's members walking around with vague memories of algebraic formulas and geometric diagrams, and clear memories of hating them.

I carried this problem around in my head basically the whole time. I would wake up with it first thing in the morning, I would be thinking about it all day, and I would be thinking about it when I went to sleep. Without distraction I would have the same thing going round and round in my mind. (Recalling the degree of focus and determination that eventually yielded the proof of Fermat's Last Theorem.)

I confess that Fermat's Theorem as an isolated proposition has very little interest for me, for a multitude of such theorems can easily be set up, which one could neither prove nor disprove. But I have been stimulated by it to bring our again several old ideas for a great extension of the theory of numbers. Of course, this theory belongs to the things where one cannot predict to what extent one will succeed in reaching obscurely hovering distant goals. A happy star must also rule, and my situation and so manifold distracting affairs of course do not permit me to pursue such meditations as in the happy years 1796-1798 when I created the principal topics of my Disquisitiones arithmeticae. But I am convinced that if good fortune should do more than I expect, and make me successful in some advances in that theory, even the Fermat theorem will appear in it only as one of the least interesting corollaries. {In reply to Olbers' attempt in 1816 to entice him to work on Fermat's Theorem. The hope Gauss expressed for his success was never realised.}

I don't know if you're in my range, but I'd sure like to take you back to my domain.

I don't know my limits.

I don't suppose", Cheris said to the servitor, "you know what resources I'm allowed to include in my proposal?" ... "Any plan you can induce Kel command to accept is permitted," it said: not quite a tautology.

Derrière la série de Fourier, d'autres séries analogues sont entrées dans la domaine de l'analyse; elles y sont entrees par la même porte; elles ont été imaginées en vue des applications. After the Fourier series, other series have entered the domain of analysis; they entered by the same door; they have been imagined in view of applications.

I don't believe in the glory and the dream. I believe in statistics.

I entered Princeton University as a graduate student in 1959, when the Department of Mathematics was housed in the old Fine Hall. This legendary facility was marvellous in stimulating interaction among the graduate students and between the graduate students and the faculty. The faculty offered few formal courses, and essentially none of them were at the beginning graduate level. Instead the students were expected to learn the necessary background material by reading books and papers and by organising seminars among themselves. It was a stimulating environment but not an easy one for a student like me, who had come with only a spotty background. Fortunately I had an excellent group of classmates, and in retrospect I think the "Princeton method" of that period was quite effective.

If I wanted you to understand, I would have explained it better ~ Aarush Kashyap

If college admissions officers are going to encourage kids to take the same AP math class, why not statistics? Almost every career (whether in business, nonprofits, academics, law, or medicine benefits from proficiency in statistics. Being an informed, responsible citizen requires a sound knowledge of statistics, as politicians, reporters, and bloggers all rely on "data" to justify positions. [p.98]

If I were king, I would redress an abuse which cuts back, as it were, one half of human kind. I would have women participate in all human rights, especially those of the mind.

If market pricing is the only legitimate test of quality, why are we still bothering with proven theorems? Why don't we just have a vote on whether a theorem is true? To make it better we'll have everyone vote on it, especially the hundreds of millions of people who don't understand the math. Would that satisfy you?

If my path is right, let it be your path; if your path is right, let it be my path!

If there is anything that can bind the mind of man to this dreary exile of our earthly home and can reconcile us with our fate so that one can enjoy living,—then it is verily the enjoyment of the mathematical sciences and astronomy.

If our sides were unequal our angles might be unequal. Instead of its being sufficient to feel, or estimate by sight, a single angle in order to determine the form of an individual, it would be necessary to ascertain each angle by the experiment of Feeling. But life would be too short for such a tedious groping. The whole science and art of Sight Recognition would at once perish; Feeling, so far as it is an art, would not long survive; intercourse would become perilous or impossible; there would be an end to all confidence, all forethought; no one would be safe in making the most simple social arrangements; in a word, civilization would relapse into barbarism.

If scientific reasoning were limited to the logical processes of arithmetic, we should not get very far in our understanding of the physical world. One might as well attempt to grasp the game of poker entirely by the use of the mathematics of probability.

I have been able to solve a few problems of mathematical physics on which the greatest mathematicians since Euler have struggled in vain ... But the pride I might have held in my conclusions was perceptibly lessened by the fact that I knew that the solution of these problems had almost always come to me as the gradual generalization of favorable examples, by a series of fortunate conjectures, after many errors. I am fain to compare myself with a wanderer on the mountains who, not knowing the path, climbs slowly and painfully upwards and often has to retrace his steps because he can go no further—then, whether by taking thought or from luck, discovers a new track that leads him on a little till at length when he reaches the summit he finds to his shame that there is a royal road by which he might have ascended, had he only the wits to find the right approach to it. In my works, I naturally said nothing about my mistake to the reader, but only described the made track by which he may now reach the same heights without difficulty.

Infinity exist unfortnately what will happen if we accept it?? After all numbers are taken what happens?? We will start with Omega+1 Then Omega+Omega+1... Think on this, this is the infinitive road, I gave it to you but what you will do?

... I left Caen, where I was living, to go on a geological excursion under the auspices of the School of Mines. The incidents of the travel made me forget my mathematical work. Having reached Coutances, we entered an omnibus to go to some place or other. At the moment when I put my foot on the step, the idea came to me, without anything in my former thoughts seeming to have paved the way for it, that the transformations I had used to define the Fuchsian functions were identical with those of non-Euclidean geometry. I did not verify the idea; I should not have had time, as upon taking my seat in the omnibus, I went on with a conversation already commenced, but I felt a perfect certainty. On my return to Caen, for convenience sake, I verified the result at my leisure.

I'm really good with problems. I can solve a differential equation in my head. I chew through trig angles like candy. I know this, and it just makes it worse. Because I don't know how to solve this one.

In geometry, whenever we had to find the area of a circle, pi * radius squared, I would get really hungry for pie. Square pie.

[In high school] my interests outside my academic work were debating, tennis, and to a lesser extent, acting. I became intensely interested in astronomy and devoured the popular works of astronomers such as Sir Arthur Eddington and Sir James Jeans, from which I learnt that a knowledge of mathematics and physics was essential to the pursuit of astronomy. This increased my fondness for those subjects.

Infinity...is used in physics simply as a shorthand for "a very big number.

In mathematics, in physics, people are concerned with what you say, not with your certification. But in order to speak about social reality, you must have the proper credentials, particularly if you depart from the accepted framework of thinking. Generally speaking, it seems fair to say that the richer the intellectual substance of a field, the less there is a concern for credentials, and the greater is concern for content.

INTROSPECTION AND INSANITY: A GODELIAN PROBLEM I think it can have suggestive value to translate Godel's Theorem into other domains, provided one specifies in advance that the translations are metaphorical and are not intended to be taken literally. That having been said, I see two major ways of using analogies to connect Godel's Theorem and human thoughts. One involves the problem of wondering about one's sanity. How can you figure out if you are sane? This is a Strange Loop indeed. Once you begin to question your own sanity, you can get trapped in an ever-tighter vortex of self-fulfilling prophecies, though the process is by no means inevitable. Everyone knows that the insane interpret the world via their own peculiarly consistent logic; how can you tell if your own logic is 'peculiar' or not, given that you have only your own logic to judge itself? I don't see any answer. I am just reminded of Godel's second Theorem, which implies that the only versions of formal number theory which assert their own consistency are inconsistent...

In my opinion, defining intelligence is much like defining beauty, and I don’t mean that it’s in the eye of the beholder. To illustrate, let’s say that you are the only beholder, and your word is final. Would you be able to choose the 1000 most beautiful women in the country? And if that sounds impossible, consider this: Say you’re now looking at your picks. Could you compare them to each other and say which one is more beautiful? For example, who is more beautiful— Katie Holmes or Angelina Jolie? How about Angelina Jolie or Catherine Zeta-Jones? I think intelligence is like this. So many factors are involved that attempts to measure it are useless. Not that IQ tests are useless. Far from it. Good tests work: They measure a variety of mental abilities, and the best tests do it well. But they don’t measure intelligence itself.

In the judgment of the most competent living mathematicians, Fraulein Noether was the most significant mathematical genius thus far produced since the higher education of women began.

I remember our childhood days when life was easy and math problems hard. Mom would help us with our homework and dad was not at home but at work. After our chores, we’d go to the old fort museum with clips in our hair and pure joy in our hearts. You, sister, wore the bangles that you, brother, got as a prize from the Dentist. “Why the bangles?” the Dentist asked, surprised, for boys picked the stickers of cars instead. “They’re for my sisters,” you said. Mom would treat us to a bottle of Coke, a few sips each. Then, we’d buy the sweet smelling bread from the same white van and hand-in-hand, we’d walk to our small flat above the restaurant. I remember our childhood days. Do you remember them too?

Réduites à des théories générales, les mathématiques seraient une belle forme sans contenu. Reduced to general theories, mathematics would be a beautiful form without content.

{Replying to G. H. Hardy's suggestion that the number of a taxi (1729) was 'dull', showing off his spontaneous mathematical genius} No, it is a very interesting number; it is the smallest number expressible as a sum of two cubes in two different ways, the two ways being 13 + 123 and 93 + 103.